In △ABC, point P∈ AB
is so that AP:BP=1:3 and point M is the midpoint of segment
CP
. Find the area of △ABC if the area of △BMP is equal to 21m2.

Answers

Answer 1

Answer:

56 m²

Explanation:

A diagram can be helpful.

Triangles with the same altitude will have areas proportional to the length of their bases.

The altitude from B to PC is the same for triangles BMP and BMC, so they have areas that are in the same proportion as MP : MC. Since M is the midpoint of CP, MP = MC and ABMP = ABMC = 21 m². Then ...

... ACPB = 21 m² + 21 m² = 42 m²

The altitude from C to AB is the same for triangles CPA and CPB, so those triangles have areas in the sampe proportion as AP : BP = 1 : 3. Then ...

... ACPA : ACPB = PA : PB = 1 : 3

... ACPA : 42 m² = 1 : 3

So, the area of ∆CPA is 1/3 of 42 m², or 14 m². The area of ABC is the sum of the areas of CPA and CPB, so is ...

... AABC = ACPA + ACPB = 14 m² + 42 m²

... AABC = 56 m²

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Answers

Answer:

Step-by-step explanation:

A car company claims that its cars achieve an average gas mileage of at least 26 miles per gallon. A random sample of five cars form this company have an average gas mileage of 25.2 miles per gallon and a standard deviation of 1 mile per gallon. At α=0.06, can the company’s claim be supported, assuming this is a normally distributed data set?

Answers

Answer with explanation:

Let $\mu$ be the population mean.

Null hypothesis : $H_0:\mu\geq26$

Alternative hypothesis : $H_1:\mu<26$

Since the alternative hypothesis is left tailed, so the test is a left-tailed test.

Sample size : n=5 <30 , so we use t-test.

Test statistic: $t=\frac{\overline{x}-\mu}{(\sigma)/(√(n))}$

$t=(25.2-26)/((1)/(√(5)))\approx-1.79$

Critical t-value for t= $t_(n-1, \alpha)=t_(4,0.06)=1.9712$

Since, the absolute value of t (1.79) is less than the critical t-value , so we fail to reject the null hypothesis.

Hence, we have sufficient evidence to support the company's claim.

What is negative b minus 4b

Answers

-5b
is the the answer
- b - 4b = - 5b

5 23 18 8 4
Order of operations

Answers

Answer:

no u

Step-by-step explanation:

Answer:

hmm lets see sorry i cant help i wish i could but its been a while

Step-by-step explanation:

Martin can travel 174 miles in 3 hours. At this rate, how far can he travel in 7.

Answers

Answer:

I believe the answer is 406 miles.

Let me know of this is the correct answer

over 6 days, Dan jogged 7.5 miles, 6 miles, 3 miles, 3 miles, 5.5 miles and 5 miles what is the mean distance that Dan jogged each day

Answers

To start add together all of the miles over 6 days. Added together it equals 30 miles.

Then take 30 miles divided by how many days.
30 divided by 6.
30 divided by 6=5
5 miles is the mean distance.

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